I have created a shapefile with multiple polygons. When I attempt to move one of the veritices with the node tool new sements automatically appear that cross the polygon and even cross the opposite poygon border to a vertex on another polygon. I can sometimes clean this up and toggle editing off. Then I "Check plygon validity" and there are no errors, but when I toggle editing again the offending segments reappear. I started again with a new QGIS project and a new shapefile layer (not snapping to the "bad" layer) and got the same problem at another location. Same problem occurs if "avoid intersecting polygons" is on or off. Snapping distance is set to 10 m, distance is >100m to the vertices that the new lines automatically go to. One, two, or three new lines may radiate from the same "offending" vertex.

Working with this new layer and project, if I close QGIS and reopen, the shapefile looks good, but the probelm reappears when I start to edit the node. I was able to delete the offending node, but it will reappear when I edit vertices weith the node tool. Help! (V 1.8, Windows). I don't recall this happening with v 1.6.

This sounds odd, have you tried changing snapping distance to e.g. 7 pixels instead? Does the problem still occur? Are you absolutely certain it's 10 m and not 10 degrees?
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underdark♦Apr 25 '13 at 13:30